I think that McMurphy's rage is aimed at Nurse Ratched's notion of control. It is this element that triggers McMurphy's anger. I think that this is reflective of how Kesey constructs the power dynamic between both. McMurphy's happiness comes from being able to disrupt the Status Quo, while Nurse Ratched's being is derived from maintaining it. From this, the simmering tension between both of them arise.
I think that the the moment that gets McMurphy "really mad" would have to be at the end of the book. Nurse Ratched's manipulation and control leads to invoke dishonor and shame when Billy is found naked with Candy. She deliberately knows what effect her words will have on him and in this feeling of shame, he kills himself. McMurphy recognizes this and it triggers in him a sense of the rage and anger that he has been experiencing towards Nurse Ratched for some time. In this, he chokes her, almost reflective of his own sense of anger at the Status Quo, the feelings he held in terms of wishing to take the life out of the controlling structure are embodied in her neck between his hands. It is the death of Billy that moves McMurphy to do more than simply seek to rile up the system, but rather seek to eliminate it once and for all, something he does in a sense of calm anger.